arXiv subjects

J. Ignacio Cirac

Publications and source records attributed to J. Ignacio Cirac.

At least 199 records · Page 11Linked to original sources

arXiv2015

Slowest local operators in quantum spin chains

We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to $M$ consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian. We first show that the Frobenius norm bounds the time scale of relaxation of the operator at high temperatures. We find operators with significantly slower relaxation than the slowest simple "hydrodynamic" mode due to energy diffusion. Then, we examine some properties of the nontrivial slow operators. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain; this system is hydrodynamically "trivial", with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity.

cond-mat.stat-mech↗

arXiv2015

Chiral topological spin liquids with projected entangled pair states

Topological chiral phases are ubiquitous in the physics of the Fractional Quantum Hall Effect. Non-chiral topological spin liquids are also well known. Here, using the framework of projected entangled pair states (PEPS), we construct a family of chiral spin liquids on the square lattice which are generalized spin-1/2 Resonating Valence Bond (RVB) states obtained from deformed local tensors with $d+i\, d$ symmetry. On a cylinder, we construct four topological sectors with even or odd number of spinons on the boundary and even or odd number of ($\mathbb{Z}_2$) fluxes penetrating the cylinder which, we argue, remain orthogonal in the limit of infinite perimeter. The analysis of the transfer matrix provides evidence of short-range (long-range) triplet (singlet) correlations as for the critical (non-chiral) RVB state. The Entanglement Spectrum exhibits chiral edge modes, which we confront to predictions of Conformal Field Theory, and the corresponding Entanglement Hamiltonian is shown to be long ranged.

cond-mat.str-el↗

arXiv2015

Efficient variational diagonalization of fully many-body localized Hamiltonians

We introduce a unitary matrix-product operator (UMPO) based variational method that approximately finds all the eigenstates of fully many-body localized (fMBL) one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed bond dimension of the UMPO ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.

cond-mat.str-el↗

arXiv2015

Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems

We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate representation of the system evolution until the stationary state is attained, the algorithm directly targets the final state, thus allowing for a faster convergence when the steady state is a MPO with small bond dimension. Our numerical simulations for several dissipative spin models over a wide range of parameters illustrate the performance of the method and show that indeed the stationary state is often well described by a MPO of very moderate dimensions.

quant-ph↗

arXiv2015

Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.

cond-mat.str-el↗

arXiv2015

Quantum dynamics of propagating photons with strong interactions: a generalized input-output formalism

There has been rapid development of systems that yield strong interactions between freely propagating photons in one dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing with photons or quantum many-body states of light, but treating such systems generally remains a difficult task theoretically. Here, we describe a novel technique in which the dynamics and correlations of a few photons can be exactly calculated, based upon knowledge of the initial photonic state and the solution of the reduced effective dynamics of the quantum emitters alone. We show that this generalized "input-output" formalism allows for a straightforward numerical implementation regardless of system details, such as emitter positions, external driving, and level structure. As a specific example, we apply our technique to show how atomic systems with infinite-range interactions and under conditions of electromagnetically induced transparency enable the selective transmission of correlated multi-photon states.

quant-ph↗

arXiv2015

Gauging quantum states: from global to local symmetries in many-body systems

We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS), we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration free gauge theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z2 gauge theory with Higgs matter.

quant-ph↗

arXiv2014

Quantum simulation of the Schwinger model: A study of feasibility

We analyze some crucial questions regarding the practical feasibility of quantum simulation for lattice gauge models. Our analysis focuses on two models suitable for the quantum simulation of the Schwinger Hamiltonian, or QED in 1+1 dimensions, which we investigate numerically using tensor networks. In particular, we explore the effect of representing the gauge degrees of freedom with finite-dimensional systems and show that the results converge rapidly; thus even with small dimensions it is possible to obtain a reasonable accuracy. We also discuss the time scales required for the adiabatic preparation of the interacting vacuum state and observe that for a suitable ramping of the interaction the required time is almost insensitive to the system size and the dimension of the physical systems. Finally, we address the possible presence of noninvariant terms in the Hamiltonian that is realized in the experiment and show that for low levels of noise it is still possible to achieve a good precision for some ground-state observables, even if the gauge symmetry is not exact in the implemented model.

quant-ph↗

arXiv2014

The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States

We present our recent results for the tensor network (TN) approach to lattice gauge theories. TN methods provide an efficient approximation for quantum many-body states. We employ TN for one dimensional systems, Matrix Product States, to investigate the 1-flavour Schwinger model. In this study, we compute the chiral condensate at finite temperature. From the continuum extrapolation, we obtain the chiral condensate in the high temperature region consistent with the analytical calculation by Sachs and Wipf.

hep-lat↗

arXiv2014

Frustration free gapless Hamiltonians for Matrix Product States

For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is local and frustration free but gapless, and its spectrum is $\R^+$. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build such uncle Hamiltonian with the same properties in the thermodynamic limit.

quant-ph↗

arXiv2014

Chiral projected entangled-pair state with topological order

We show that projected entangled-pair states (PEPS) can describe chiral topologically ordered phases. For that, we construct a simple PEPS for spin-1/2 particles in a two-dimensional lattice. We reveal a symmetry in the local projector of the PEPS that gives rise to the global topological character. We also extract characteristic quantities of the edge conformal field theory using the bulk-boundary correspondence.

cond-mat.str-el↗

arXiv2014

Algorithms for finite Projected Entangled Pair States

Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary to make the ansatz widely usable in practice. Here we analyze several algorithmic aspects of the method. On the one hand, we quantify the connection between the correlation length of the PEPS and the accuracy of its approximate contraction, and discuss how purifications can be used in the latter. On the other, we present algorithmic improvements for the update of the tensor that introduce drastic gains in the numerical conditioning and the efficiency of the algorithms. Finally, the state-of-the-art general PEPS code is benchmarked with the Heisenberg and quantum Ising models on lattices of up to $21 \times 21$ sites.

quant-ph↗

arXiv2014

Long-Distance Transfer and Routing of Static Magnetic Fields

We show how the static magnetic field of a finite source can be transferred and routed to arbitrary long distances. This is achieved by using transformation optics, which results in a device made of a material with a highly anisotropic magnetic permeability. We show that a simplified version of the device, made by a superconducting-ferromagnet hybrid, also leads to an excellent transfer of the magnetic field. The latter is demonstrated with a proof-of-principle experiment where a ferromagnet tube coated with a superconductor improves the transfer of static magnetic fields with respect to conventional methods by a 400\% factor over distances of 14cm.

cond-mat.supr-con↗

arXiv2014

Symmetries and boundary theories for chiral Projected Entangled Pair States

We investigate the topological character of lattice chiral Gaussian fermionic states in two dimensions possessing the simplest descriptions in terms of projected entangled-pair states (PEPS). They are ground states of two different kinds of Hamiltonians. The first one, $\mathcal H_\mathrm{ff}$, is local, frustration-free, and gapless. It can be interpreted as describing a quantum phase transition between different topological phases. The second one, $\mathcal H_\mathrm{fb}$ is gapped, and has hopping terms scaling as $1/r^3$ with the distance $r$. The gap is robust against local perturbations, which allows us to define a Chern number for the PEPS. As for (non-chiral) topological PEPS, the non-trivial topological properties can be traced down to the existence of a symmetry in the virtual modes that are used to build the state. Based on that symmetry, we construct string-like operators acting on the virtual modes that can be continuously deformed without changing the state. On the torus, the symmetry implies that the ground state space of the local parent Hamiltonian is two-fold degenerate. By adding a string wrapping around the torus one can change one of the ground states into the other. We use the special properties of PEPS to build the boundary theory and show how the symmetry results in the appearance of chiral modes, and a universal correction to the area law for the zero Rényi entropy.

cond-mat.str-el↗

arXiv2014

Construction of spin models displaying quantum criticality from quantum field theory

We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification. Their properties can be investigated by Monte-Carlo simulations, which enable us to study the low-temperature phase diagram and to show that it displays a region of quantum criticality. The mixed states obtained are shown to be close to the thermal state of a simple nearest neighbour Hamiltonian.

cond-mat.str-el↗

arXiv2014

Optical lattice implementation scheme of a bosonic topological model with fermionic atoms

We present a scheme to implement a Fermi-Hubbard-like model in ultracold atoms in optical lattices and analyze the topological features of its ground state. In particular, we show that the ground state for appropriate parameters has a large overlap with a lattice version of the bosonic Laughlin state at filling factor one half. The scheme utilizes laser assisted and normal tunnelling in a checkerboard optical lattice. The requirements on temperature, interactions, and hopping strengths are similar to those needed to observe the Néel antiferromagnetic ordering in the standard Fermi-Hubbard model in the Mott insulating regime.

cond-mat.str-el↗

arXiv2014

Approximating Gibbs states of local Hamiltonians efficiently with PEPS

We analyze the error of approximating Gibbs states of local quantum spin Hamiltonians on lattices with Projected Entangled Pair States (PEPS) as a function of the bond dimension ($D$), temperature ($β^{-1}$), and system size ($N$). First, we introduce a compression method in which the bond dimension scales as $D=e^{O(\log^2(N/ε))}$ if $β<O(\log (N))$. Second, building on the work of Hastings [Phys. Rev. B 73, 085115 (2006)], we derive a polynomial scaling relation, $D=\left(N/ε\right)^{O(β)}$. This implies that the manifold of PEPS forms an efficient representation of Gibbs states of local quantum Hamiltonians. From those bounds it also follows that ground states can be approximated with $D=N^{O(\log(N))}$ whenever the density of states only grows polynomially in the system size. All results hold for any spatial dimension of the lattice.

quant-ph↗

arXiv2014

Nuclear Spin Dynamics in Double Quantum Dots: Multi-Stability, Dynamical Polarization, Criticality and Entanglement

We theoretically study the nuclear spin dynamics driven by electron transport and hyperfine interaction in an electrically-defined double quantum dot (DQD) in the Pauli-blockade regime. We derive a master-equation-based framework and show that the coupled electron-nuclear system displays an instability towards the buildup of large nuclear spin polarization gradients in the two quantum dots. In the presence of such inhomogeneous magnetic fields, a quantum interference effect in the collective hyperfine coupling results in sizable nuclear spin entanglement between the two quantum dots in the steady state of the evolution. We investigate this effect using analytical and numerical techniques, and demonstrate its robustness under various types of imperfections.

cond-mat.mes-hall↗